Fig1c.tab: Data for Figure 1c. Electric field is split into real and imaginary components.

Fig2a.tab: Data for Figure 2a. Electric field is split into real and imaginary components.
Fig2b.tab: Data for Figure 2b. Raw observations, prior to binning and symmetrization.
Fig2c.tab: Data for Figure 2c. Binned and symmetrized overlap histogram, with bin coordinates Q and R provided.
Fig2d.tab: Data for Figure 2d. Electric field is split into real and imaginary components.
Fig2e.tab: Data for Figure 2e. Raw observations, prior to binning and symmetrization.
Fig2f.tab: Data for Figure 2f. Binned and symmetrized overlap histogram, with bin coordinates Q and R provided.
Fig2_xFM.tab: Measured interaction matrices J_ij and K_ij for the x-ferromagnet in Figures 2a-c and S21a, see also Section IV. The data labeled "gauged" is after the gauge transformations described in Section II.F.
Fig2_yFM.tab: Measured interaction matrices J_ij and K_ij for the y-ferromagnet in Figures 2e-d and S21b, see also Section IV. The data labeled "gauged" is after the gauge transformations described in Section II.F.

Fig3a.tab: Data for Figure 3a. Electric field is split into real and imaginary components.
Fig3b.tab: Data for Figure 3b. Electric field is split into real and imaginary components.
Fig3c.tab: Data for Figure 3c. Electric field is split into real and imaginary components.
Fig3d.tab: Data for Figure 3d. Electric field is split into real and imaginary components.
Fig3e.tab: Data for Figure 3e. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig3f.tab: Data for Figure 3f. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig3g.tab: Data for Figure 3g. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig3h.tab: Data for Figure 3h. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig3i.tab: Data for Figure 3i. Overlap values, with index labels alpha and beta provided.
Fig3i_linkage.tab: Data for dendrogram in Figure 3i. The dendrogram is encoded into a linkage matrix, see also the documentation for scipy.cluster.hierarchy.linkage.
Fig3j.tab: Data for Figure 3j. Overlap values, with index labels alpha and beta provided.
Fig3j_linkage.tab: Data for dendrogram in Figure 3j. The dendrogram is encoded into a linkage matrix, see also the documentation for scipy.cluster.hierarchy.linkage.
Fig3k.tab: Data for Figure 3k. Overlap values, with index labels alpha and beta provided.
Fig3k_linkage.tab: Data for dendrogram in Figure 3k. The dendrogram is encoded into a linkage matrix, see also the documentation for scipy.cluster.hierarchy.linkage.
Fig3l.tab: Data for Figure 3l. Overlap values, with index labels alpha and beta provided.
Fig3l_linkage.tab: Data for dendrogram in Figure 3l. The dendrogram is encoded into a linkage matrix, see also the documentation for scipy.cluster.hierarchy.linkage.

Fig4a.tab: Data for Figure 4a. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4b.tab: Data for Figure 4b. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4c.tab: Data for Figure 4c. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4d.tab: Data for Figure 4d. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4e.tab: Data for Figure 4e. Binned and symmetrized, aggregated two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4f.tab: Data for Figure 4f. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4f_JK.tab: Measured interaction matrices J_ij and K_ij for the disorder instance presented in Figures 4a,f (and Figure 3).
Fig4g.tab: Data for Figure 4g. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4g_JK.tab: Measured interaction matrices J_ij and K_ij for the disorder instance presented in Figures 4b,g.
Fig4h.tab: Data for Figure 4h. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4h_JK.tab: Measured interaction matrices J_ij and K_ij for the disorder instance presented in Figures 4c,h.
Fig4i.tab: Data for Figure 4i. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4i_JK.tab: Measured interaction matrices J_ij and K_ij for the disorder instance presented in Figures 4d,i.
Fig4j.tab: Data for Figure 4j. Binned and symmetrized, aggregated two-dimensional overlap histogram, with bin coordinates Q and R provided.
Fig4l.tab: Data for Figure 4l. Binned and symmetrized, aggregated two-dimensional magnetization histogram, with bin indices for m^x and m^y provided.
Fig4m.tab: Data for Figure 4m. Binned and symmetrized, aggregated two-dimensional magnetization histogram, with bin indices for m^x and m^y provided.

FigS1_transmission.tab: Data for cavity transmission trace in Figure S1.

FigS2_emission.tab: Data for cavity emission intensity trace in Figure S2.
FigS2_pump.tab: Data for pump power trace in Figure S2.

FigS3a.tab: Data for Figure S3a. Electric field is split into real and imaginary components.
FigS3b.tab: Data for Figure S3b. Electric field is split into real and imaginary components.
FigS3c.tab: Data for Figure S3c. Electric field is split into real and imaginary components.
FigS3d.tab: Data for Figure S3d. Electric field is split into real and imaginary components.

FigS4.tab: Data for Figure S4. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided. Each column corresponds to the labeled panel.

FigS5.tab: Data for Figure S5. Raw observations, prior to binning.

FigS6a_emission.tab: Data for cavity emission intensity trace in Figure S6a.
FigS6a_pump.tab: Data for pump power trace in Figure S6a.
FigS6bc.tab: Data for Figure S6b and S6c. Coordinate system is shared.
FigS6d.tab: Data for Figure S6d. Raw observations, prior to binning.

FigS7.tab: Data for interaction matrices in Figure S7.

FigS8.tab: Data for interaction matrices in Figure S8.

FigS9.tab: Data for Figure S9. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates Q and R provided. Data for panels a-i are in the respective files for Figure 4 of the main text.
FigS9_Js.tab: Data for Figure S9, presenting bootstrapped interaction matrices J_ij used for panels f1-i10.
FigS9_Ks.tab: Data for Figure S9, presenting bootstrapped interaction matrices K_ij used for panels f1-i10.

FigS10_FM.tab: Data for Figure S10a and S11a. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates for Q and R provided.
FigS10_SG.tab: Data for Figure S10b and S11b. Binned and symmetrized two-dimensional overlap histogram, with bin coordinates for Q and R provided.
FigS10c.tab: Data for Figure S10c. Binned overlap distributions, with bin coordinates for q provided. Since different system sizes have different number of overlap bins, the bin coordinates and probability densities are padded with np.nan.
FigS10d.tab: Data for Figure S10d. X values and error bars for all system sizes and temperatures presented.

FigS11: All data is contained in FigS10_FM.tab and FigS10_SG.tab.

FigS12be.tab: Data for Figure S12b-e. Binder ratios for the respective quantities, with coordinates for J and T provided.
FigS12fi.tab: Data for Figure S12f-i. Binder ratios for the respective quantities, with coordinates for J and T provided.

FigS13.tab: Data for Figure S13. Binned and symmetrized two-dimensional overlap histogram, with bin indices for Q and R provided.

FigS14.tab: Data for Figure S14 as x and y coordinates.

FigS15.tab: Data for Figure S15 as x and y coordinates.

FigS16.tab: Data for both panels of Figure S16 as x and y coordinates

FigS17.tab: Data for Figure S17. Binned and symmetrized, aggregated two-dimensional overlap histogram, with bin coordinates Q and R provided. Data for panel a is in Fig4e.tab

FigS18.tab: Data for Figure S18. Binned and symmetrized, aggregated two-dimensional overlap histogram, with bin coordinates Q and R provided.

FigS19.tab: Data for Figure S19. Binned and symmetrized two-dimensional overlap histogram, with bin indices for Q and R provided.

FigS20.tab: Data for Figure S20. Binned and symmetrized two-dimensional overlap histogram, with bin indices for Q and R provided.

FigS21a.tab: Data for Figure S21a. Raw observations, prior to binning.
FigS21b.tab: Data for Figure S21b. Raw observations, prior to binning.

FigS22a.tab: Raw data for Figure S22a.
FigS22b.tab: Raw data for Figure S22b.

FigS23_GOE_ev.tab: Data for Figure S23a (red line).
FigS23_GOE_split.tab: Data for Figure S23b (red line).
FigS23_Js.tab: Data for Figures S23 and S27, presenting interaction matrices J_ij for all 123 disorder instances.
FigS23_Ks.tab: Data for Figures S23 and S27, presenting interaction matrices K_ij for all 123 disorder instances.
FigS23_positions.tab: Additional data for Figures S23 and S26, presenting the positions for the atomic vertices for all 123 disorder instances. Each pair of (x,y) columns corresponds to an individual disorder instance.
FigS23_GOE_analysis.py: Python code for theory curves of Figure S23.

FigS24a.tab: Data for Figure S24a. Raw observations, prior to binning.
FigS24b.tab: Data for Figure S24b. Each column is the histogram for an individual disorder instance.

FigS25a.tab: Data for Figure S25a.
FigS25b.tab: Data for Figure S25b. Mean(K) values and its error bars for all system sizes and temperatures presented.
FigS25c.tab: Data for Figure S25c. Var(K) values and its error bars for all system sizes and temperatures presented.

FigS26a.tab: Data for Figure S26a. Mean(K) values and its error bars for all system sizes presented.
FigS26b.tab: Data for Figure S26b. Var(K) values and its error bars for all system sizes presented.

FigS27.tab: Data for Figure S27. Binned and symmetrized two-dimensional overlap histogram, with bin indices for Q and R provided. Each column corresponds to an individual disorder instance.

ParallelTempering_python.py: Python code used for generating data of Figure S13.

meanField.jl: Julia script for performing mean field trajectory simulations, used in Figures 4, S4, S9, S17, S18, S19, S20, and S26.

ParrellelTempering.py: Python code base for simulation of 3D model, as used in Sec. II.D.
PTScript.py: Python script to execute parallel tempering for this 3D model code.
ParallelTempering.ipynb: Jupyter notebook to analyze the results from 3D parallel tempering.

library.jl: Julia library for large system parallel tempering simulations, used in Sec. V (except for V.C) and Figures S10, S11, and S12.
PT_script.jl: Julia script to execute large system parallel tempering simulations.
branch_states-library.jl: Julia library for large system parallel tempering simulations, dedicated to study of ultrametricity (explicit saving of spin configurations). Used for Figure S25.
branch_states-PT_script.jl: Julia script to execute ultrametricity-dedicated large system parallel tempering simulations.
sample-moSKK008_params.json: Example file illustrating typical settings used to configure these large system parallel tempering simulations.

replicon.ipynb: Jupyter notebook for finding the replica-symmetric saddle point and its stability (replicon mass), i.e. Figures S14 and S15.
compare.ipynb: Jupyter notebook for numerically solving and extremizing the 1-step replica-symmetry breaking free energy, i.e. Figure S16.